Q: How can I give my sister a break from taking care of our elderly dad when I live hundreds of miles away? She refuses to let me help, because she has always been controlling. Its her way or the highway, but she needs a break.
A: I'm glad you wrote to tell "the other side." This is not so unusual. Caregivers know the person they are caring for is used to the way they do things and will be upset by change, yet they desperately need a break from their duties.
As is often the case, sibling issues from childhood can get to be part of the situation, as well. This sounds a bit like what is happening here. If your sister has always been controlling, this is another way to control. But she does need a break, though she may truly feel she is doing what is best for your father.
Ideally, you'd have a third party conversation - say over a conference call, if you can't do it in person - and someone, maybe a counselor, could help all of you decide what is best.
However, reality is such that this doesn't sound likely. If you can't even get her to answer a letter or phone call, it's going to be tough to help.
Hopefully, you can find some way to communicate and tell her that since she needs a break, you can help pay for someone to relieve her at home. In-home health agencies do this, and then the argument that your dad would be disoriented by going to be with you (very possibly true) wouldn't hold water.
Lack of communication and control issues abound in these situations and about all I can tell you is that you aren't alone in this. There are many in your shoes.
Try the offer of paid help and see if you get a response. If she won't even respond to that, then you'll have to detach, or go in person and see what really can be done.